1. Field of the Invention
The present invention relates to the field of prisms, wavelength division multiplexers, and optical integrated circuits. More specifically, it relates to methods of dispersing a polychromatic electromagnetic wave into its constituent wavelength An components.
2. Description of Related Art
A photonic crystal is a periodic structure consisting typically of two dielectric materials with high dielectric contrast (e.g., semiconductor and air), and with geometrical feature sizes comparable to or smaller than light wavelengths of interest. As an engineered structure or artificially engineered material, a photonic crystal can exhibit optical properties not commonly found in natural substances. Extensive research has led to the discovery of several classes of photonic crystal structures for which the propagation of electromagnetic radiation is forbidden in certain frequency ranges (photonic band gaps, or PBGs). More recently, it has also been realized that electromagnetic radiation with frequency just outside the photonic band gaps can propagate in photonic crystals with characteristics that are quite different from those of ordinary optical materials. Recently, Kosaka and co-workers, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami published an article titled xe2x80x9cSuperprism phenomena in photonic crystals: Toward microscale lightwave circuitsxe2x80x9d, Journal of Lightwave Technology, 17 (11): 2032-2038 (1999). In the article, Kosaka showed that they had demonstrated a xe2x80x9csuperprismxe2x80x9d phenomenon in a three-dimensional photonic crystal. They reported that two light beams, with slightly different wavelengths (0.99 xcexcm and 1 xcexcm), exhibited a 50xc2x0 divergence inside the photonic crystal. The same pair of beams entering a conventional optical material at the same angle would diverge by less than 1xc2x0 after incidence. This unusually large color-dispersion capability is called the superprism or ultra-refractive effect. The photonic crystal that was the subject of the demonstration is a complex three-dimensional (3D) structure consisting of, from bottom to top: (1) a silicon substrate, (2) a silicon dioxide buffer layer patterned with a hexagonal array of holes formed by electron-beam lithography, and (3) alternating layers of amorphous silicon and silicon dioxide sputtered on top of the patterned buffer layer. It is believed that. NEC, NTT, and the Tohoku University in Japan sponsored the work performed. It is believed that the Tohoku University made the devices tested using E-beam (electron-beam) lithography to form a hexagonal lattice pattern on a silicon dioxide buffer layer grown on top of a silicon substrate. That step was followed by the deposition of amorphous silicon and silicon dioxide in alternating layers. A typical structure consists of 20 or so pairs of silicon/silicon dioxide layers. The silicon/silicon dioxide layers follow the contour of the E-beam patterned buffer layer and form a three-dimensional structure. The many steps in the process suggest that the devices produced were made at high cost.
The unusual propagation characteristics of electromagnetic waves with frequency just outside the photonic band gaps (PBGs) have been analyzed by a number of researchers. Lin et al. xe2x80x9crecognize the highly nonlinear dispersion of PBG materials near Brilluoin zone edges and utilize the dispersion to achieve strong prism actionxe2x80x9d (xe2x80x9cHighly dispersive photonic band-gap prism,xe2x80x9d S. Y. Lin, V. M. Hietala, L.
Wang and E. D. Jones, Optics Letters, 21(21), pp 1771-1773, 1996). Notomi performed theoretical analysis and demonstrated xe2x80x9cthat light propagation in strongly modulated two-dimensional (2D)/3D photonic crystals become refractionlike in the vicinity of photonic band gap.xe2x80x9d (xe2x80x9cTheory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,xe2x80x9d M. Notomi, Phys. Rev. B, 62(16), pp 10696-10705, 2000). Miller et al. stated that in xe2x80x9cregion just outside the main reflection region there is strong group velocity dispersions, causing different wavelength of light to travel at different angles through the dielectric stack.xe2x80x9d (xe2x80x9cMethod for dispersing light using multilayered structures,xe2x80x9d D.
A. B. Miller et al., U.S. patent application Ser. No. 20020018298). Lin et al. found that xe2x80x9cvery strong dependence of dielectric constant, and hence index of refraction, on photon energy near the bandgap allows photonic crystals to be used to form highly dispersive prisms and other optical elements.xe2x80x9d (S. Y. Lin et al., U.S. patent application No. 20010012149). All of these works recognize the strong dispersion of electromagnetic waves with frequencyjust outside the photonic band gaps (PBGs).
The invention shows that strong wavelength dispersion, known as the superprism effect or ultra-refraction, can be found in one-dimensional (one-dimensional) photonic crystals for entire photonic bands rather than near the band edges only. In the lowest frequency photonic band, ultra-refraction occurs near the edge of the Brillouin zone. In higher photonic bands, where wavelengths are always comparable to or shorter than photonic crystal feature sizes, ultra-refraction can be found for the entire band, or a significant portion of the entire band, rather than just near the band edges Oust outside photonic band gaps). The use of full bands rather than only band edges broadens the ultra-refraction wavelength range considerably. The use of full bands is preferred, as transmission tends to diminish near the band edges just outside photonic band gaps where reflection occurs. The use of higher bands also allows the use of photonic crystals with larger feature sizes, thereby reducing fabrication requirements. In a prism-like geometry, electromagnetic waves dispersed by the one-dimensional photonic crystal exhibit angular dependence on wavelength which is much closer to being linear, making this effect much easier to use than the highly non-linear dispersions near the band gap. The properties of the ultra-refractive one-dimensional photonic crystal prism can be tuned by varying design parameters such as incidence angle, exit surface angle, and layer widths. The mathematical analysis of a one-dimensional photonic crystal is well understood, and therefore the design procedure is simple. In addition to the foregoing, a one-dimensional photonic crystal prism is easier to fabricate than a 2D or 3D photonic crystal prisms. For optical and infrared wavelengths, they can be made on semiconductor wafers (e.g., silicon or gallium arsenide), which also allows for the possibility of monolithic integration with other micro optical components. For applications to longer wavelengths (such as millimeter waves), one-dimensional photonic crystal prisms could be made by bonding pre-formed wafers together.
An important reason why we are able to exploit fill-band ultra-refraction in one-dimensional photonic crystals is that it is easy to design one-dimensional photonic crystals with simple band structures that monotonically vary with frequency and wave vector. In 2D and 3D photonic crystals, photonic band structure can be considerably more complicated, and can sometimes exhibit features such as crossings or anti-crossings, or a multiplicity of bands, which makes the exploitation of full-band ultra-refraction more difficult. However, appropriately engineered 2D/3D photonic crystals can exhibit fill-band (or at least partial band, rather than band-edge only) ultra-refraction, albeit at a greater cost due to increased complexity.